The Extended EBIS is currently going through final development and offline testing and will replace RHIC EBIS as a main ion injector for both RHIC and NASA Space Radiation Laboratory in the beginning of 2023. Due to its longer ion trap, the Extended EBIS will enhance the maximum available beam intensity of Au32+ions by 40 - 50% compared to RHIC EBIS. With a further upgrade, the Extended EBIS will also produce polarized 3He2+ ions for the future electron-ion collider. Two attractive options for external ion sources of singly charged ions which can significantly improve the operational flexibility and stability of Extended EBIS are a picosecond laser ion source and a cluster ion source. A laser with high rep-rate can produce quasi continuous singly charged ion beams from elements of solid targets for periods of tens of milliseconds, making it possible to take advantage of the ability of the EBIS to trap singly charged ions in accumulation injection mode. For most of gaseous elements, a source of cluster ions is quite an attractive option. Cluster ion beams have multiple advantages for external injection into EBIS trap in comparison with atomic ion beams.